Question

Many oxides of nitrogen have positive values for the standard free energy of formation. Using NO as an example, explain why this is the case.

Short answer

Many oxides of nitrogen, such as NO, have positive values for the standard free energy of formation (ΔGf°) due to their endothermic formation, which requires energy to break the strong N-N triple bond. The entropy change (ΔS) during their formation is not significant enough to compensate for the positive enthalpy change (ΔH). Consequently, the formation of these compounds is thermodynamically not favorable under standard conditions, as demonstrated by the calculation of ΔGf°(NO) = 27.5 kJ/mol.

Step-by-step solution

1. Definition of Standard Free Energy of Formation

The standard free energy of formation, denoted as ΔGf°, is the change in Gibbs free energy when one mole of a compound is formed from its elements in their most stable forms (i.e., standard states) in a given environment, usually 1 atm pressure and 298.15 K temperature.

2. Factors Influencing the Value of Standard Free Energy of Formation

The standard free energy of formation for a reaction depends on two factors: enthalpy change (ΔH) and the temperature-dependent entropy change (ΔS). The relationship between these factors and free energy is given by: \[ ΔG = ΔH - TΔS \] In this formula, ΔG represents the free energy change, ΔH represents the enthalpy change, T represents the temperature in Kelvin, and ΔS represents the entropy change.

3. Enthalpy and Entropy Changes for Oxides of Nitrogen

In the case of oxides of nitrogen, the enthalpy of formation (ΔHf°) is generally positive, indicating that the formation of these compounds requires energy, i.e., they are endothermic reactions. This is because nitrogen is a very stable molecule and breaking the strong triple bond between nitrogen atoms requires a considerable amount of energy. The entropy change (ΔS) for the formation of these compounds is not significant enough to compensate for the positive enthalpy change.

4. Standard Free Energy of Formation for Nitric Oxide (NO)

Taking nitric oxide (NO) as an example, the standard enthalpy of formation (ΔHf°) and the standard entropy change (ΔS°) can be looked up in a table or determined experimentally. Values for the formation of NO at 298.15 K and 1 atm are: ΔHf°(NO) = 90.37 kJ/mol ΔS°(NO) = 210.76 J/mol•K Using these values, we can calculate the standard free energy of formation (ΔGf°) for NO at 298.15 K as follows: \[ ΔGf°(NO) = ΔHf°(NO) - TΔS°(NO) \] \[ ΔGf°(NO) = 90.37 kJ/mol - (298.15 K)(0.21076 kJ/mol•K) \] \[ ΔGf°(NO) = 90.37 kJ/mol - 62.87 kJ/mol \] \[ ΔGf°(NO) = 27.5 kJ/mol \] The positive value of ΔGf°(NO) indicates that the formation of NO is not spontaneous under standard conditions.

5. Conclusion

Many oxides of nitrogen, like NO, have positive values for the standard free energy of formation because their formation is endothermic, requiring energy to break the strong N-N triple bond. The entropy change during the formation is not significant enough to compensate for the positive enthalpy change, resulting in a positive value for ΔGf. This suggests that the formation of these compounds is thermodynamically not favorable under standard conditions.